The starting angle θθ of a pendulum does not affect its period for θ<<1θ<<1. At higher angles, however, the period TT increases with increasing θθ.
The relation between TT and θθ can be derived by solving the equation of motion of the simple pendulum (from F=ma)
−gsinθ=lθ¨−gainθ=lθ¨
For small angles, θ≪1,θ≪1, and hence sinθ≈θsinθ≈θ. Hence,
θ¨=−glθθ¨=−glθ
This second-order differential equation can be solved to get θ=θ0cos(ωt),ω=gl−−√θ=θ0cos(ωt),ω=gl. The period is thus T=2πω=2πlg−−√T=2πω=2πlg, which is independent of the starting angle θ0θ0.
For large angles, however, the above derivation is invalid. Without going into the derivation, the general expression of the period is T=2πlg−−√(1+θ2016+...)T=2πlg(1+θ0216+...). At large angles, the θ2016θ0216 term starts to grow big and cause
Answer:
The slower the intended velocity, the closer the force expressed comes to equalling the linear inertia of the load (i.e. the amount of force needed to hold the weight motionless). From Equation 1, force is inversely proportional to time
Answer:
1. Lateral inversion is a phenomenon in which left appears to be right and vice versa. It is due to direction that light follows when it strikes a reflecting surface, generally a mirror.
These are the letters which don't show lateral inversion A,H,O,T,U
2. USES OF CONCAVE MIRROR
They are used as shaving mirrors to see a larger image of the face.
Dentists use concave mirrors to view large images of the teeth of the patients.
USES OF CONVEX MIRROR
It is is used as a rear view mirror in vehicles.
It is used as a vigilance mirror.
